Tambahkan transisi fermionik ke pool konfigurasi

Di sini kita mendemonstrasikan fungsionalitas untuk memperbesar pool konfigurasi elektronik yang diperoleh dari aksi operator transisi pada setiap konfigurasi elektronik.

Kita tunjukkan cara menambahkan lompatan satu elektron dengan tipe:

$$c^\dagger_{p\sigma} c_{q\sigma} |\textbf{x} \rangle$$

untuk $p, q = 1, ..., N_\textrm{orb}$ dan $\sigma \in \{ \uparrow, \downarrow\}$, serta untuk semua $|\textbf{x} \rangle$ dalam batch konfigurasi elektronik. Kita mulai dengan membangkitkan batch konfigurasi elektronik acak:

# Added by doQumentation — installs the packages this notebook needs if they are missing
import importlib.util

_needed = {"numpy": "numpy", "qiskit_addon_sqd": "qiskit-addon-sqd"}
_missing = [pip for module, pip in _needed.items()
            if importlib.util.find_spec(module) is None]
# One at a time, so a package that fails to install does not block the others
for _pip in _missing:
    %pip install -q {_pip}
if not _missing:
    print("\u2713 All required packages are installed")

import numpy as np

n_qubits = 8
n_orb = n_qubits // 2

rand_seed = 22
np.random.seed(rand_seed)

# Generate some random bitstrings for testing
def random_bitstrings(n_samples, n_qubits):
    return (
        np.round(np.random.rand(n_samples, n_qubits))
        .astype("int")
        .astype("bool")
    )

bitstring_matrix = random_bitstrings(100, n_qubits)

Operator eksitasi ditentukan di dalam array numpy yang panjangnya sama dengan jumlah node fermionik (atau qubit). Setiap elemen array harus berupa string yang bisa bernilai:

• 'I': Identity

• '+': Operator pembentukan (creation)

• '-': Operator peluruhan (annihilation)

Kita bangkitkan semua kemungkinan transisi satu elektron (di antara spesies spin yang sama).

transitions_single = np.array(
    [
        ["I" for i in range(2 * n_orb)]
        for j in range(4 * (n_orb**2 - n_orb) // 2 + 1)
    ]
)
count = 1
for i in range(n_orb):
    for j in range(i + 1, n_orb):
        # spin up
        transitions_single[count, i] = "+"
        transitions_single[count, j] = "-"
        count += 1
        transitions_single[count, i] = "-"
        transitions_single[count, j] = "+"
        count += 1

        # spin down
        transitions_single[count, i + n_orb] = "+"
        transitions_single[count, j + n_orb] = "-"
        count += 1
        transitions_single[count, i + n_orb] = "-"
        transitions_single[count, j + n_orb] = "+"
        count += 1

print(transitions_single)

[['I' 'I' 'I' 'I' 'I' 'I' 'I' 'I']
 ['+' '-' 'I' 'I' 'I' 'I' 'I' 'I']
 ['-' '+' 'I' 'I' 'I' 'I' 'I' 'I']
 ['I' 'I' 'I' 'I' '+' '-' 'I' 'I']
 ['I' 'I' 'I' 'I' '-' '+' 'I' 'I']
 ['+' 'I' '-' 'I' 'I' 'I' 'I' 'I']
 ['-' 'I' '+' 'I' 'I' 'I' 'I' 'I']
 ['I' 'I' 'I' 'I' '+' 'I' '-' 'I']
 ['I' 'I' 'I' 'I' '-' 'I' '+' 'I']
 ['+' 'I' 'I' '-' 'I' 'I' 'I' 'I']
 ['-' 'I' 'I' '+' 'I' 'I' 'I' 'I']
 ['I' 'I' 'I' 'I' '+' 'I' 'I' '-']
 ['I' 'I' 'I' 'I' '-' 'I' 'I' '+']
 ['I' '+' '-' 'I' 'I' 'I' 'I' 'I']
 ['I' '-' '+' 'I' 'I' 'I' 'I' 'I']
 ['I' 'I' 'I' 'I' 'I' '+' '-' 'I']
 ['I' 'I' 'I' 'I' 'I' '-' '+' 'I']
 ['I' '+' 'I' '-' 'I' 'I' 'I' 'I']
 ['I' '-' 'I' '+' 'I' 'I' 'I' 'I']
 ['I' 'I' 'I' 'I' 'I' '+' 'I' '-']
 ['I' 'I' 'I' 'I' 'I' '-' 'I' '+']
 ['I' 'I' '+' '-' 'I' 'I' 'I' 'I']
 ['I' 'I' '-' '+' 'I' 'I' 'I' 'I']
 ['I' 'I' 'I' 'I' 'I' 'I' '+' '-']
 ['I' 'I' 'I' 'I' 'I' 'I' '-' '+']]

Sekarang kita terapkan operator transisi ke konfigurasi di bitstring_matrix:

from qiskit_addon_sqd.fermion import enlarge_batch_from_transitions

bitstring_matrix_aug = enlarge_batch_from_transitions(
    bitstring_matrix, transitions_single
)

print(bitstring_matrix_aug.shape)
print(bitstring_matrix_aug)

(723, 8)
[[False False False ... False False  True]
 [False  True False ...  True False False]
 [ True  True  True ...  True False  True]
 ...
 [ True False  True ... False False  True]
 [ True  True  True ...  True False  True]
 [False False False ... False False  True]]